Flutter flight test involves the evaluation of the airframes aeroelastic stability by applying artificial excitation on the aircraft lifting surfaces. The subsequent responses are captured and analyzed to extract the frequencies and damping characteristics of the system. However, noise contamination, turbulence, non-optimal excitation of modes, and sensor malfunction in one or more sensors make it time-consuming and corrupt the extraction process. In order to expedite the process of identifying and analyzing aeroelastic modes, this study implements a time-delay embedded Dynamic Mode Decomposition technique. This approach is complemented by Robust Principal Component Analysis methodology, and a sparsity promoting criterion which enables the automatic and optimal selection of sparse modes. The anonymized flutter flight test data, provided by the fifth author of this research paper, is utilized in this implementation. The methodology assumes no knowledge of the input excitation, only deals with the responses captured by accelerometer channels, and rapidly identifies the aeroelastic modes. By incorporating a compressed sensing algorithm, the methodology gains the ability to identify aeroelastic modes, even when the number of available sensors is limited. This augmentation greatly enhances the methodology's robustness and effectiveness, making it an excellent choice for real-time implementation during flutter test campaigns.